Systems and methods for providing enhanced volume-weighted average price trading

ABSTRACT

Systems and methods for providing trading using an eVWAP price in an illiquid market are provided. In an illiquid market there may be little or no actual trades. During a trading period, the eVWAP price is therefore determined from not only trades, but also unmatched bids and offers. The eVWAP price is determined when new information becomes available or at a specified time interval. The final eVWAP price is determined when the sampling period ends. Once the final eVWAP price is determined, the value of the final eVWAP price is published for use as a price to settle a contract.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. provisional application No. 60/512,029, filed Oct. 17, 2003, which is hereby incorporated by reference herein in its entirety.

BACKGROUND OF THE INVENTION

The present invention relates to systems and methods for calculating an enhanced volume-weighted average price, and more particularly to trading systems that allow traders to place orders on average price contracts based on trades, bids, and offers.

Electronically based trading systems have gained widespread popularity over the years. Such trading systems are frequently used for trading items ranging from financial instruments (such as stocks, bonds, currency, futures, contracts, etc.) to used household goods (such as old records, baseball cards, antiques, etc.). In many of these trading systems, bid/offer-hit/lift processes are used to negotiate a sale of a given item. In connection with such processes, bids and/or offers for items are entered into a trading system and a hit or lift is submitted in response to a bid or offer, respectively, to agree to a sale, or a purchase.

Historically, traders use benchmarks to evaluate their trades. Determining the volume-weighted average price (hereinafter the “VWAP”) is one of the most common trade evaluation benchmarks. Traders, brokers, institutional investors, and managers determine the quality of their trades by calculating the VWAP and comparing the VWAP to the prices of which their trades were executed. For example, if a trader purchased a stock today at a price lower than the current cumulative VWAP, the trader bought the stock at a good price—i.e., better than the average buyer of the stock. On the other hand, if the trader bought the stock at a price higher than the VWAP, then the trader overpaid for the stock relative to other buyers of the day. Traders often monitor the VWAP to, for example, predict when short term buying and selling opportunities may arise.

There are markets that provide trading data such that the VWAP may be calculated. One embodiment of an interactive trading system that allows traders to trade on the VWAP is described in co-pending, commonly-assigned U.S. patent application Ser. No. 10/678,582, filed Oct. 2, 2003, and U.S. Provisional Application No. 60/415,843, filed Oct. 2, 2002, which are hereby incorporated by reference herein in their entireties. Trading on the VWAP may provide an opportunity for buyers and sellers to buy or sell items at a price that is the VWAP price or at a price that closely tracks the VWAP price.

However, the conventional VWAP may not be calculated for an illiquid market or a temporarily illiquid market which has little or no volume of trades. Illiquid markets and temporarily illiquid markets that have little or no volume of trades do not allow traders to buy and sell items without causing a significant and possibly disproportionate price change.

Therefore, it would be desirable to provide traders with an opportunity to evaluate instruments traded in illiquid markets or temporarily illiquid markets using an approach for calculating an enhanced VWAP price. It would also be desirable to provide an enhanced VWAP price, for an instrument, that may be used as a basis for trading derivatives of that instrument (i.e., the enhanced VWAP price may be used to mark a closing price for which derivative contracts may settle).

SUMMARY OF THE INVENTION

It is therefore an object of this invention to provide traders with an opportunity to evaluate instruments traded in illiquid markets or temporarily illiquid markets using an approach for calculating an enhanced VWAP price (hereinafter “eVWAP”). It is also an object of this invention to provide an eVWAP price, for an instrument, that may be used as a basis for trading derivatives of that instrument (i.e., the eVWAP price may be used to mark a closing price for which derivative contracts may settle).

These and other objects are accomplished in accordance with the principles of the present invention by providing systems and methods that provide traders with an eVWAP price that uses unmatched bid and offer prices to support or back up traded price volumes over a predetermined sampling period or trading period, thereby alleviating the above-mentioned difficulties. Such an approach may be used for illiquid markets or temporarily illiquid markets where there may be little or no actual trades. The approach for calculating the eVWAP price may include adjusting the eVWAP price using data (e.g., price and size information) from unmatched bids and offers. Unmatched bids and offers may be those bids and offers that have not been hit or lifted.

As used herein, the “eVWAP” or “eVWAP price” is a weighted average price based on trade data (e.g., the prices and volume of trades) and unmatched bid and offer data (e.g., bid price, offer price, etc.) done on one or more items within a specified sampling period. As the specified sampling period progresses, all trade prices and sizes, bid prices and sizes, and offer prices and sizes of an item are collected. In response to collecting the data entered by traders, the eVWAP may be calculated based on the collected trade, bid, and offer data as they appear during the sampling period. For example, an eVWAP price may be recalculated when new trade, bid, or offer data becomes available, and may be published to the market as the eVWAP price builds during the sampling period.

In an illiquid market, publishing the eVWAP price during the sampling period may attract further liquidity. Since the eVWAP price includes bid and offer data, in addition to trade data (which is all the VWAP generally includes), changes in the eVWAP price will be more active than the VWAP and may encourage traders to enter bids and offers. Additional bids and offers may in turn create a more liquid market.

In some embodiments, the collected bids and offers may be limited to a particular collar (i.e., a predetermined price range in which bids and offers may be accepted). Bids and offers outside of the collar are preferably not used in the calculation of the eVWAP price. For example, all trade data may be used to calculate the eVWAP price, while only bids and offers within the collar are used to calculate the eVWAP price. The collar may be adjusted as the eVWAP price builds in reference to a cumulative “reference price.” The “reference price” is preferably calculated as the eVWAP sampling period progresses (e.g., in real-time or at another suitable periodic interval). Although data from unmatched bids and offers may be used to calculate the eVWAP price, it should be noted that an actual trade may have a substantially larger influence on the eVWAP price than unmatched bids and offers. That is, an actual trade may reduce the significance of bid and offer values in the eVWAP price determined at the end of the sampling period.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects and advantages of the invention will be apparent upon consideration of the following detailed description, taken in conjunction with accompanying drawings, in which like reference refers to like parts throughout, and in which:

FIG. 1 is a flow diagram of a main process that may be used to provide an enhanced volume-weighted average price with certain embodiments of the present invention;

FIG. 2 is a block diagram of a system that may be used to implement processes and functions of certain embodiments of the present invention; and

FIG. 3 is a block diagram of a workstation, a server, and a back office clearing center that may be used to implement the processes and functions of certain embodiments of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

This invention relates to creating systems and methods for calculating an enhanced volume-weighted average price based on trades, bids, and offers. The following embodiment of the invention relates to the electronic trading of fixed income related instruments—e.g., such as the United States Treasuries, United Kingdom Gilts, European Government Treasuries, and Emerging Market debts, swaps, repos, etc. This invention may also be used for the electronic trading of securities or other financial instruments, such as stocks or currencies, and is not limited only to the trading of fixed income related instruments. Nevertheless, this embodiment does not limit the invention to this particular subject matter. Rather, it is provided for illustration of the invention and not to limit it to a particular commodity or market.

It should also be noted that although the following embodiment of the invention relates specifically to the trading of a single instrument, such as United States 30 Year U.S. Treasury bonds, this embodiment is not limited only to the trading of a single instrument. Rather, the invention may also be applied to the trading of a basket of instruments. For example, traders may trade on the eVWAP price on the net price movements of the current two-year United States Treasury bills, three-year and five-year United States Treasury notes, and ten-year United States Treasury bonds.

An eVWAP price may be calculated that provides traders with an opportunity to trade in illiquid markets or temporarily illiquid markets where there may be little or no actual trades. The eVWAP price may use unmatched bid and offer prices to support or back up traded price volumes over a predetermined sampling period or trading period. This approach may include adjusting the eVWAP price using data (e.g., price and size information) from unmatched bids and offers of an instrument. The eVWAP price may be used as a basis for trading derivatives of that instrument (i.e., the eVWAP price may be used to mark a closing price for which derivative contracts may settle).

As mentioned previously, the collected bids and offers may be limited to a particular collar such that those bids and offers outside of the collar are preferably not used in calculation of the eVWAP price. However, if desired, a collar may not be imposed and all bids and offers may be used in calculation of the eVWAP price. If used, the collar may be adjusted as the eVWAP price builds in reference to a cumulative “reference price.” The “reference price” is preferably calculated before the eVWAP sampling period progresses. The reference price may be the bid-offer spread at the starting time, which is preferably calculated using the following equation:

${{eVWAP}_{0} = \frac{\left( {{bid\_ price}_{0} \times {bid\_ size}_{0}} \right) + \left( {{offer\_ price}_{0} \times {offer\_ size}_{0}} \right)}{{bid\_ size}_{0} + {offer\_ size}_{0}}},$ where eVWAP₀ is the initial reference price, and bid_price₀, bid_size₀, offer_price₀, and offer_price₀ are the bid price, bid size, offer price, and offer size, respectively, of an instrument at the start time of the eVWAP sampling period.

If there is not a bid-offer spread at the start of the sampling period, the reference price is the last traded price (i.e., eVWAP₀=last_trade_price) and the total trade size is the last traded size (i.e., total_trade_size₀=last_trade_size). It should be noted that if the last traded price is lower than the current bid or higher than the current offer, then the start point will be the bid or offer, respectively.

If there is no last traded price, then the reference price is the previous closing or reference price (i.e., eVWAP₀=closing_price) and the total trade size is set to 1 (i.e., total_trade_size₀=1).

The eVWAP price may be recalculated as new data relating to trades, bids, and offers is received. When the new data received is a trade, the traded price is multiplied by the trade size and added to the indicative price (i.e., eVWAP_(t−1)) multiplied by the previous total trade size. The result is divided by the total size traded. When a trade is received, the current eVWAP price may be calculated using the following equation:

${{eVWAP}_{t} = \frac{\left( {{trade\_ price}_{t} \times {trade\_ size}_{t}} \right) + \left( {{eVWAP}_{t - 1} \times {total\_ trade}{\_ size}_{t - 1}} \right)}{{total\_ trade}{\_ size}_{t}}},$ where total_trade_size_(t)=total_trade_size_(t−1)+trade_size_(t).

When the new data received is a bid, the eVWAP price is adjusted towards the bid. For example, if the bid is lower than the indicative price, the updated eVWAP price is also adjusted lower. When the new data received is an offer, the eVWAP price is adjusted towards the offer. For example, if the offer is lower than the indicative price, the updated eVWAP price is also adjusted lower. Although the algorithm may be applicable to any kind of instrument and market type, in the preferred embodiment, the instrument is traded in a normal market.

When a bid and an offer are received simultaneously, the eVWAP price is adjusted according to the accumulated bid and offer adjustments. That is, the adjustment is equivalent to the sum of the bid and offer adjustments. If the indicative price is between the bid and the offer, then the bid adjustment generates a negative number, while the offer adjustment generates a positive number. If the existing indicative price is higher than the newly received bid and the newly received offer, then the bid adjustment and the offer adjustment both generate a negative number. If the existing indicative price is lower than the newly received bid and the newly received offer, then the bid adjustment and the offer adjustment both generate a positive number. When a bid and/or offer is received, the current eVWAP price is preferably calculated using the following equation:

${eVWAP}_{t} = \left( {{eVWAP}_{t - 1} + \frac{\begin{matrix} {{bid\_ flag}*\left( \frac{{bid\_ size}_{t}^{{bid\_ size}{\_ flag}}}{{total\_ trade}{\_ size}_{t - 1}} \right)^{{trade\_ ratio}{\_ flag}}*} \\ {{bid\_ size}{\_ ratio}^{{bid\_ ratio}{\_ flag}}*\left( {{bid}_{t} - {eVWAP}_{t - 1}} \right)} \end{matrix}}{\left( {1 + {{bid\_ scaling}{\_ factor}*{{{bid}_{t} - {eVWAP}_{t - 1}}}}} \right)^{bid\_ exponent}} + \frac{\begin{matrix} {{offer\_ flag}*\left( \frac{{offer\_ size}_{t}^{{offer\_ size}{\_ flag}}}{{total\_ trade}{\_ size}_{t - 1}} \right)^{{trade\_ ratio}{\_ flag}}*} \\ {{offer\_ size}{\_ ratio}^{{offer\_ ratio}{\_ flag}}*\left( {{offer}_{t} - {eVWAP}_{t - 1}} \right)} \end{matrix}}{\left( {1 + {{offer\_ scaling}{\_ factor}*{{{offer}_{t} - {eVWAP}_{t - 1}}}}} \right)^{offer\_ exponent}}} \right)$

These two algorithms may be combined to calculate an eVWAP price that takes into account trades, bids, and offers as they appear during the specified sampling period. The eVWAP, during the sampling period, is preferably calculated using the following algorithm:

${eVWAP}_{t} = {{{trade\_ flag}*\left( \frac{\begin{matrix} \left( {{{trade\_ price}_{t}*{trade\_ size}_{t}} +} \right. \\ \left. {{eVWAP}_{t - 1}*{total\_ trade}{\_ size}_{t - 1}} \right) \end{matrix}}{{total\_ trade}{\_ size}_{t}} \right)} + {{bidoffer\_ flag}*\left( {{eVWAP}_{t - 1} + \frac{\begin{matrix} {{bid\_ flag}*\left( \frac{{bid\_ size}_{t}^{{bid\_ size}{\_ flag}}}{{total\_ trade}{\_ size}_{t - 1}} \right)^{{trade\_ ratio}{\_ flag}}*} \\ {{bid\_ size}{\_ ratio}^{{bid\_ ratio}{\_ flag}}*\left( {{bid}_{t} - {eVWAP}_{t - 1}} \right)} \end{matrix}}{\left( {1 + {{bid\_ scaling}{\_ factor}*{{{bid}_{t} - {{eVWAP}_{t - 1}\left.  \right)^{bid\_ exponent}}}}}} \right.} + \frac{\begin{matrix} {{offer\_ flag}*\left( \frac{{offer\_ size}_{t}^{{offer\_ size}{\_ flag}}}{{total\_ trade}{\_ size}_{t - 1}} \right)^{{trade\_ ratio}{\_ flag}}*} \\ {{offer\_ size}{\_ ratio}^{{offer\_ ratio}{\_ flag}}*\left( {{offer}_{t} - {eVWAP}_{t - 1}} \right)} \end{matrix}}{\left( {1 + {{offer\_ scaling}{\_ factor}*{{{offer}_{t} - {{eVWAP}_{t - 1}\left.  \right)^{offer\_ exponent}}}}}} \right.}} \right)}}$ where:

-   total_trade_size_(t)=total_trade_size_(t−1)+trade_size_(t)); -   trade_flag={0,1}; -   bidoffer_flag={0,1}; -   offer_flag={0,1}; -   bid_flag={0,1}; -   bid_size_flag={0,1}; -   offer_size_flag={0,1}; -   trade_ratio_flag={0,1}; -   bid_ratio_flag={0,1}; -   offer_ratio_flag={0,1}; -   |bid_(t)−eVWAP_(t−1)| is the absolute value of the difference     between bid_(t) and eVWAP-_(t−1); -   |offer_(t)−eVWAP_(t−1)| is the absolute value of the difference     between offer_(t) and eVWAP_(t−1); and -   bid_scaling_factor, offer_scaling_factor, bid_size_ratio,     offer_size_ratio, bid_exponent, and offer_exponent are other     parameters.

The values set for the other parameters may depend upon the market in which the eVWAP is operating. For example, certain factors, such as the size, liquidity, volatility, and any other suitable factors of the market, may play a role in determining the values for these other parameters. Once the values for these other parameters in a particular market are set, these values may remain constant for that market throughout the sampling period.

As shown above in the eVWAP algorithm, the “size ratio” (e.g., bid_size_ratio and offer_size_ratio) may be used to show the importance of bid and offer data with respect to trade data and is preferably a constant value. The “size ratio,” along with other parameters, does not need to be a constant value and may be a function of other terms or parameters. In some embodiments, bids and offers may be given equal weight. It should also be noted that the effect of bids and offers to adjust the eVWAP price decreases with the total traded size.

The eVWAP_(t−1) is preferably calculated as the eVWAP sampling period progresses (e.g., in real-time or at another suitable interval for a certain period). As shown, the effect of bids and offers to adjust the eVWAP price decreases with the exponent of the absolute value of the difference between the bid/offer price and the indicative price (or eVWAP_(t−1)). The impact on the eVWAP will decrease with the increase of the difference between the bid/offer price and the indicative price because the difference between the bid/offer price and the indicative price is in the denominator of the algorithm. That is, bid/offer prices that are closer to the indicative price will produce a greater adjustment to the eVWAP because bid/offer prices closer to the indicative price are likely more accurate indicators of how the eVWAP should be adjusted. The “scaling factor” (e.g., bid_scaling_factor and offer_scaling_factor) may be a multiplier, such as a multiplier of the discount rate, and is preferably a constant value. The scaling factor may be used to inflate or deflate the importance of the proximity between the bid/offer price and the indicative price.

Flags may also be used to indicate the type of data that is being received, such as, for example, trading data, bid data, offer data, etc. Each flag may be set to a value such as a “0” to indicate that the flag is turned off or a “1” to indicate that the flag is turned on. An example of settings for various flags is shown in Table 1.

TABLE 1 Action Flag Trade trade_flag = {0, 1} If the next information received is a trade, then trade_flag = 1, bidoffer_flag = 0, bid_flag = 0, and offer_flag = 0. Otherwise (no trade), trade_flag = 0. Bid bidoffer_flag = {0, 1} and bid_flag = {0, 1} If the received data is related to a bid, then bidoffer_flag = 1, bid_flag = 1, and trade_flag = 0. Otherwise (no bid), bid_flag = 0. Offer bidoffer_flag = {0, 1} and offer_flag = {0, 1} If the received data is related to an offer, then bidoffer_flag = 1, offer_flag = 1, and trade_flag = 0. Otherwise (no offer), offer_flag = 0. Simultaneous bidoffer_flag = {0, 1}, bid_flag = {0, 1}, Bid and Offer and offer_flag = {0, 1} If the received information is both a bid and an offer, then bidoffer_flag = 1, bid_flag = 1, offer_flag = 1, and trade_flag = 0. Bid Size and bid_size_flag ={0, 1}, offer_size_flag = {0, 1} Offer Size Bid_size_flag and offer_size_flag are used to set the size ratio to bid_size_(t)/total_trade_size_(t−1) or to 1/total_trade_size_(t−1) as bid_size⁰ = 1. Similarly, offer_size⁰ = 1 for offer_size_flag = 0. The “size flag” may be set if it is desirable to factor in the size of the bid/offer. For example, in the beginning of a sampling period the size flag may be set to zero to dampen the impact bids/offers have on eVWAP since the size ratio will result in a number less than zero (i.e., 1/total_trade_size_(t−1)). It may be desirable to dampen the impact bids/offers have on the eVWAP in the beginning because there will be little volume since it is an illiquid market or a temporarily illiquid market. At times, accounting for the bid/offer size may create undesirable spikes in the eVWAP price. Trade Ratio trade_ratio_flag = {0, 1} trade_ratio_flag enables or disables the terms: $\frac{{bid\_ size}_{t}^{{bid\_ size}{\_ flag}}}{{total\_ trade}{\_ size}_{t - 1}}\mspace{25mu}{and}\mspace{25mu}\frac{{offer\_ size}_{t}^{{offer\_ size}{\_ flag}}}{{total\_ trade}{\_ size}_{t - 1}}$ When trade_ratio_flag = 1: $\begin{matrix} {\left( \frac{{bid\_ size}_{t}^{{bid\_ size}{\_ flag}}}{{total\_ trade}{\_ size}_{t - 1}} \right)^{1} = {\frac{{bid\_ size}_{t}^{{bid\_ size}{\_ flag}}}{{total\_ trade}{\_ size}_{t - 1}}\mspace{20mu}{and}}} \\ {{\left( \frac{{offer\_ size}_{t}^{{offer\_ size}{\_ flag}}}{{total\_ trade}{\_ size}_{t - 1}} \right)^{1} = \frac{{offer\_ size}_{t}^{{offer\_ size}{\_ flag}}}{{total\_ trade}{\_ size}_{t - 1}}}\mspace{20mu}} \end{matrix}\quad$ When trade_ratio_flag = 0, ${\begin{matrix} {\left( \frac{{bid\_ size}_{t}^{{bid\_ size}{\_ flag}}}{{total\_ trade}{\_ size}_{t - 1}} \right)^{0} = {1\mspace{25mu}{and}}} \\ {{\left( \frac{{offer\_ size}_{t}^{{offer\_ size}{\_ flag}}}{{total\_ trade}{\_ size}_{t - 1}} \right)^{0} = 1}\mspace{25mu}} \end{matrix}\quad}\quad$ The trade_ratio_flag may be used to adjust the impact on the eVWAP of the bid/offer size as compared with the total size of the trade.

An example of settings for various other parameters is shown in Table 2. The settings of these parameters in Table 2 may be optional and the values may be chosen in any way that is desirable.

TABLE 2 Action Variable If bid_exponent = 0 bid_(t) > eVWAP_(t−1) If offer_exponent = 0 offer_(t) < eVWAP_(t−1)

In some embodiments, lower and upper bounds may be set for the bid and offer prices. In this way, the bids and offers may be limited to a particular collar. For example, the upper bound for bid and offer prices may be calculated using the following equation:

${{bid\_ upper}{\_ bound}} = {{eVWAP}_{t} + \frac{1}{\begin{matrix} {{{bid\_ scaling}{\_ factor}*{bid\_ exponent}} -} \\ {{bid\_ scaling}{\_ factor}} \end{matrix}}}$ ${{offer\_ upper}{\_ bound}} = {{eVWAP}_{t} + \frac{1}{\begin{matrix} {{{offer\_ scaling}{\_ factor}*{offer\_ exponent}} -} \\ {{offer\_ scaling}{\_ factor}} \end{matrix}}}$ Similarly, the lower bound for bid and offer prices may be, for example:

${{bid\_ lower}{\_ bound}} = {{eVWAP}_{t} - \frac{1}{\begin{matrix} {{{bid\_ scaling}{\_ factor}*{bid\_ exponent}} -} \\ {{bid\_ scaling}{\_ factor}} \end{matrix}}}$ ${{offer\_ lower}{\_ bound}} = {{eVWAP}_{t} - \frac{1}{\begin{matrix} {{{offer\_ scaling}{\_ factor}*{offer\_ exponent}} -} \\ {{offer\_ scaling}{\_ factor}} \end{matrix}}}$ However, any other suitable approach for calculating upper and lower bounds may also be used. The upper_bound equations may calculate the maximum point and the lower_bound equations may calculate the minimum point for the above-mentioned eVWAP algorithm for any scaling_factor values and exponent values. Based at least in part on the determined maximum and minimum points, the scaling factor value and exponent factor value may be set. For some chosen scaling_factor values and exponent values, the derivative of the above-mentioned eVWAP algorithm may not lead to determining a maximum and minimum point. In this scenario, another approach may be used to calculate the upper and lower bounds. For example, a percentage deviation from the reference price may be used as the upper and lower bounds.

In some embodiments, bid sizes and offer sizes may not be included in the algorithm for calculating the eVWAP price. This may be achieved by setting the bid_size_flag and the offer_size-flag to zero.

One embodiment of an eVWAP trading process that may be used in accordance with the principles of the present invention is illustrated in process 10 of FIG. 1. In practice, one or more steps shown may be combined with other steps, performed in any suitable order, or deleted. At step 12, a predetermined sampling period or trading period may begin. At step 14, the starting value for the reference price (or eVWAP₀) may be set. As described above, the starting value may be calculated from the bid-offer spread, the last traded price and last traded size, the current bid if the last traded price is lower than the current bid, the current offer if the last traded price is lower than the current offer, the previous closing price and setting the total trade size to 1, or in any other suitable manner.

As described above, the eVWAP may be recalculated during the sampling period as new trade, bid, or offer data becomes available (i.e., the eVWAP may be recalculated in real-time). The eVWAP may also be recalculated at periodic time intervals. As shown in step 16, if the updates to the eVWAP take place at specified or periodic time intervals, a determination may be made as to whether a specified time interval has elapsed at step 18. The specified time intervals may be every ‘n’ seconds, every ‘n’ minutes, every ‘n’ hours or any other suitable function of time. In response to the specified time interval elapsing, the eVWAP may be calculated at step 22.

If the updates to the eVWAP does not take place at specified or periodic time intervals, then, at step 20, the eVWAP may be recalculated by determining if new trade, bid, or offer information becomes available. New bid or offer information may be new bids or offers. New bid or offer information may also be reflected in changes of the price, the size, or both the price and size of previously entered bids or offers. If new information does become available, then the eVWAP may be calculated at step 22 in accordance with the algorithm described above in paragraph 26 or by any other suitable algorithm. As described above, steps of process 10 may be deleted. For example, steps 16 and 18 may be deleted and step 20 may be performed immediately after step 14.

In response to determining that a specified time interval has not elapsed at step 18, in response to determining that new trade, bid, or offer information has not become available at step 20, or in response to calculating the eVWAP at step 22, a determination may be made as to whether the sampling period has ended at step 24. If the sampling period has not ended then process 10 may return to step 16 and follow the steps described above. Once the sampling period has ended, the final eVWAP_(t) may be calculated at step 26 in accordance with the algorithm described above in paragraph 26 or by any other suitable algorithm.

At step 28, the final eVWAP_(t) may be published to the market. The final eVWAP_(t) may be published to the market in any suitable form. For example, the final eVWAP_(t) may be published by e-mail, by fax, on a ticker, on television, by posting the value to a server, by posting the value to a web site or by any other suitable form of publication. If the final eVWAP_(t) is published by being posted to a server, the value may be posted to a local server, to an FTP server, to a third-party vendor's server (e.g., Reuters®, Bloomberg®, or any other third-party vendor), or to any other suitable server. The final eVWAP price may then be used as a basis for trading derivatives of an instrument (i.e., the eVWAP price may be used to mark a closing price for which derivative contracts may settle).

An electronic trading application may be provided to provide traders with the eVWAP price. The eVWAP price may be recalculated to account for trades, bids, and offers as received during the eVWAP specified sampling period. It will be understood that the electronic trading application may be any suitable, software, hardware, or both configured to implement the features of the present invention. The electronic trading application may be located at a central location (e.g., a central server). In another suitable approach, the electronic trading application may reside among different locations (e.g., a network).

In one particular embodiment, the electronic trading application may include client-side software, hardware, or both. For example, the electronic trading application may encompass one or more Web-pages or Web-page portions (e.g., via any suitable encoding, such as XML, Cold Fusion, etc.).

Although the electronic trading application is described herein as being implemented on user computer equipment, this is only illustrative. The electronic trading application may be implemented on any suitable platform (e.g., personal computer, palmtop computer, laptop computer, personal digital assistant, cellular phone, etc.) to provide such features.

Referring to FIG. 2, an exemplary system 100 for implementing the present invention is shown. As illustrated, system 100 may include one or more trading workstations 102. Workstations 102 may be local or remote, and are connected by one or more communications links 104 to a computer network 106 that is linked via a communications link 108 to a server 110.

In system 100, server 110 may be any suitable server, processor, computer, or data processing device, or combination of the same. Computer network 106 may be any suitable computer network including the Internet, an intranet, a wide-area network (WAN), a local-area network (LAN), a wireless network, a digital subscriber line (DSL) network, a frame relay network, an asynchronous transfer mode (ATM) network, a virtual private network (VPN), or any combination of any of the same. Communications links 104 and 106 may be any communications links suitable for communicating data between workstations 102 and server 110, such as network links, dial-up links, wireless links, hard-wired links, etc. Workstations 102 enable a trader to engage in the trading process. Workstations 102 may be personal computers, laptop computers, mainframe computers, dumb terminals, data displays, Internet browsers, personal digital assistants (PDAs), two-way pagers, wireless terminals, portable telephones, etc., or any combination of the same.

A back office clearing center 114 may also be connected to server 110 of the trading system via a communications link 112. Clearing center 114 may be any suitable equipment, such as a computer, or combination of the same, for causing trades to be cleared and/or verifying that trades are cleared. If desired, server 110 may contain multiple processors. Communications link 112 may be any communications link suitable for communicating data between server 110 and back office clearing center 114, such as network links, dial-up links, wireless links, hard-wired links, etc.

The server, the back office clearing center, and one of the workstations, which are depicted in FIG. 2, are illustrated in more detail in FIG. 3. Referring to FIG. 3, workstation 102 may include processor 202, display 204, input device 206, and memory 208, which may be interconnected. In a preferred embodiment, memory 208 contains a storage device for storing a workstation program for controlling processor 220. Memory 226 also preferably contains an eVWAP trading application 210 according to the invention.

eVWAP trading application 210 may preferably include an application program interface (not shown), or, as described above, eVWAP trading application 210 may be resident in the memory of server 110. In this embodiment, the electronic trading application may contain eVWAP trading application 210 and an application program interface (not shown) as a discrete application from the electronic trading application which also may be included therein. The only distribution to the trader may then be a Graphical User Interface which allows the trader to interact with eVWAP trading application 210 resident at server 110.

Processor 202 uses the workstation program to present on display 204 the electronic trading application and trading information relating to market conditions received through communication link 104 and trading commands and values transmitted by a trader of workstation 102. Furthermore, input device 206 may be used to manually enter commands and values in order for these commands and values to be communicated to the electronic trading application.

Server 110 may include processor 220, display 222, input device 224, and memory 226, which may be interconnected. In a preferred embodiment, memory 226 contains a storage device for storing information relating to market conditions received through communication link 108 or through other links, and also receives trading commands and values transmitted by one or more traders. The storage device further contains a server program for controlling processor 220. Processor 220 uses the server program to transact the purchase and sale of the fixed income related instruments and to perform the above-mentioned systems and methods.

Back office clearing center 114 may include processor 228, display 230, input device 232, and memory 234, which may be interconnected. In a preferred embodiment, memory 234 contains a storage device for storing a clearing program for controlling processor 228. Processor 228 may use the clearing program to complete the transactions that are entered into by the traders. Processor 228 uses the clearing program to further verify that the transactions are completed and cleared.

Thus, systems and methods for providing enhanced volume-weighted average price trading are provided. Persons skilled in the art will appreciate that the present invention can be practiced by other than the described embodiments, which are presented for purposes of illustration and not of limitation, and that the present invention is limited only by the claims which follow. 

1. A method comprising the steps of: at least one programmed computer receiving, over a duration of a sampling period, market data for at least one financial instrument, wherein the received market data comprises executed trades and unmatched orders for the at least one financial instrument, and wherein the executed trades and the unmatched orders comprise respective sizes and prices; over the duration of the sampling period, the at least one programmed computer iteratively recalculating for the at least one financial instrument an enhanced volume-weighted average price based at least in part on the received market data, wherein the iterative recalculating of the enhanced volume-weighted average price comprises the steps of: at a point in time during the duration of the sampling period, calculating the enhanced volume-weighted average price based at least in part on at least one of the received executed trades and the received unmatched orders; and at a subsequent point in time during the duration of the sampling period, calculating the enhanced volume-weighted average price based at least in part on: a) the resulting enhanced volume-weighted average price calculated at the point in time, and b) a price of another of the received unmatched orders, wherein there is a difference between the price of the another unmatched order and the resulting enhanced volume-weighted average price calculated at the point in time, and wherein an effect of the another unmatched order to adjust the resulting enhanced volume-weighted average price calculated at the subsequent point in time decreases as the difference increases; and at an end of the sampling period, the at least one programmed computer communicating via a communications network to at least another programmed computer a last recalculated value for the enhanced volume-weighted average price.
 2. The method of claim 1, wherein at each iteration, the enhanced volume-weighted average price is recalculated as: ${{trade\_ flag}*\left( \frac{\begin{matrix} \left( {{{trade\_ price}_{t}*{trade\_ size}_{t}} +} \right. \\ \left. {{eVWAP}_{t - 1}*{total\_ trade}{\_ size}_{t - 1}} \right) \end{matrix}}{{total\_ trade}{\_ size}_{t}} \right)} + {{bidoffer\_ flag}*{\left( {{eVWAP}_{t - 1} + \frac{\begin{matrix} {{bid\_ flag}*\left( \frac{{bid\_ size}_{t}^{{bid\_ size}{\_ flag}}}{{total\_ trade}{\_ size}_{t - 1}} \right)^{{trade\_ size}{\_ flag}}*} \\ {{bid\_ size}{\_ ratio}^{{bid\_ ratio}{\_ flag}}*\left( {{bid}_{t} - {eVWAP}_{t - 1}} \right)} \end{matrix}}{\left( {1 + {{bid\_ scaling}{\_ factor}*{{{bid}_{t} - {eVWAP}_{t - 1}}}}} \right)^{bid\_ exponent}} + \frac{\begin{matrix} {{offer\_ flag}*\left( \frac{{offer\_ size}_{t}^{{offer\_ size}{\_ flag}}}{{total\_ trade}{\_ size}_{t - 1}} \right)^{{trade\_ size}{\_ flag}}*} \\ {{offer\_ size}{\_ ratio}^{{offer\_ ratio}{\_ flag}}*\left( {{offer}_{t} - {eVWAP}_{t - 1}} \right)} \end{matrix}}{\left( {1 + {{offer\_ scaling}{\_ factor}*{{{offer}_{t} - {eVWAP}_{t - 1}}}}} \right)^{offer\_ exponent}}} \right).}}$
 3. The method of claim 1, wherein iteratively recalculating the enhanced volume-weighted average price over the duration of the sampling period comprises recalculating the enhanced volume-weighted average price each time a specified time interval elapses during the duration of the sampling period.
 4. The method of claim 1, wherein receiving, over the duration of the sampling period, the market data comprises: receiving at another point in time at least one of the unmatched orders; and receiving at a further point in time, that is subsequent to the another point in time, a change in at least one of the price and the size of the unmatched order received at the another point in time.
 5. The method of claim 1, wherein calculating the enhanced volume-weighted average price at the subsequent point in time further comprises the step of calculating the enhanced volume-weighted average price based at least in part on at least one weight that is applied, in part, to the price of the another unmatched order, wherein the at least one weight reduces an effect of the another unmatched order to adjust the resulting enhanced volume-weighted average price calculated at the subsequent point in time.
 6. The method of claim 1, wherein the another unmatched order causes the resulting enhanced volume-weighted average price calculated at the point in time to adjust towards the price of the another unmatched order such that the resulting enhanced volume-weighted average price calculated at the subsequent point in time is closer to the price of the another unmatched order than the resulting enhanced volume-weighted average price calculated at the point in time.
 7. The method of claim 6, wherein the price of the another unmatched order is lower than the resulting enhanced volume-weighted average price calculated at the point in time; and wherein the resulting enhanced volume-weighted average price calculated at the subsequent point in time is lower than the resulting enhanced volume-weighted average price calculated at the point in time.
 8. The method of claim 6, wherein the price of the another unmatched order is higher than the resulting enhanced volume-weighted average price calculated at the point in time; and wherein the resulting enhanced volume-weighted average price calculated at the subsequent point in time is higher than the resulting enhanced volume-weighted average price calculated at the point in time.
 9. The method of claim 6, wherein calculating the enhanced volume-weighted average price at the subsequent point in time further comprises the steps of: determining a first value by subtracting the resulting enhanced volume-weighted average price calculated at the point in time from the price of the another unmatched order, the first value having one of a negative sign and a positive sign; determining a second value based at least in part on the first value, the second value having the same sign as the first value; and adding the second value to the resulting enhanced volume-weighted average price calculated at the point in time.
 10. The method of claim 1, wherein the method further comprises the step of: based at least in part on a bid-offer spread for the at least one financial instrument, determining a starting value for the enhanced volume-weighted average price; and wherein calculating, at the point in time, the enhanced volume-weighted average price further comprises calculating the enhanced volume-weighted average price based at least in part on the starting value.
 11. The method of claim 1, wherein calculating the enhanced volume-weighted average price at the subsequent point in time further comprises the step of calculating the enhanced volume-weighted average price based at least in part on a cumulative value that comprises the size of at least one of the received executed trades, wherein an effect of the another unmatched order to adjust the resulting enhanced volume-weighted average price calculated at the subsequent point in time decreases as a size of the cumulative value increases.
 12. The method of claim 1, wherein iteratively recalculating the enhanced volume-weighted average price over the duration of the sampling period further comprises the steps of: at another point in time, calculating the enhanced volume-weighted average price based at least in part on the price of a further one of the received unmatched orders and not on the size of the further unmatched order; and at a further point in time, that is subsequent to the another point in time, calculating the enhanced volume-weighted average price based at least in part on the price and the size of a still further one of the received unmatched orders.
 13. The method of claim 1, further comprising the step of: filtering out from the received market data the unmatched orders having prices that are not within a predetermined price range such that the filtered out unmatched orders are not used in recalculating the enhanced volume-weighted average price over the duration of the sampling period.
 14. The method of claim 1, wherein iteratively recalculating the enhanced volume-weighted average price over the duration of the sampling period comprises recalculating the enhanced volume-weighted average price as the market data is received over the duration of the sampling period.
 15. The method of claim 1, wherein the received unmatched orders comprise at least one of bids and offers for the at least one financial instrument.
 16. The method of claim 1, wherein calculating the enhanced volume-weighted average price at the subsequent point in time further comprises the steps of: determining a first value by subtracting the resulting enhanced volume-weighted average price calculated at the point in time from the price of the another unmatched order, the first value having one of a negative sign and a positive sign; determining a second value based at least in part on the first value, the second value having the same sign as the first value; and adding the second value to the resulting enhanced volume-weighted average price calculated at the point in time.
 17. The method of claim 16, wherein calculating the enhanced volume-weighted average price at the subsequent point in time further comprises the step of determining a third value based at least in part on the difference between the price of the another unmatched order and the resulting enhanced volume-weighted average price calculated at the point in time; and wherein determining the second value comprises the step of dividing, in part, the first value by the third value.
 18. The method of claim 17, wherein calculating the enhanced volume-weighted average price at the subsequent point in time further comprises the step of determining a fourth value by dividing the first value by a cumulative value that comprises the size of at least one of the received executed trades; and wherein determining the second value comprises the step of dividing, in part, the fourth value by the third value.
 19. The method of claim 18, wherein calculating the enhanced volume-weighted average price at the subsequent point in time further comprises the step of determining a fifth value by multiplying the fourth value by the size of the another unmatched order; and wherein determining the second value comprises the step of dividing, in part, the fifth value by the third value.
 20. The method of claim 1, wherein the method further comprises the step of: based at least in part on a last traded price for the at least one financial instrument, determining a starting value for the enhanced volume-weighted average price; and wherein calculating, at the point in time, the enhanced volume-weighted average price further comprises calculating the enhanced volume-weighted average price based at least in part on the starting value.
 21. The method of claim 1, wherein the method further comprises the steps of: determining at a start of the sampling period that: there is an outstanding unmatched bid for the at least one financial instrument, there is no outstanding unmatched offer for the at least one financial instrument, and there is a last traded price for the at least one financial instrument; determining that the last traded price is lower than a price of the outstanding unmatched bid; and based at least in part on determining that the last traded price is lower than the price of the outstanding unmatched bid, setting a starting value for the enhanced volume-weighted average price to be the price of the outstanding unmatched bid; and wherein calculating, at the point in time, the enhanced volume-weighted average price further comprises calculating the enhanced volume-weighted average price based at least in part on the starting value.
 22. The method of claim 1, wherein the method further comprises the steps of: determining at a start of the sampling period that: there is an outstanding unmatched offer for the at least one financial instrument, there is no outstanding unmatched bid for the at least one financial instrument, and there is a last traded price for the at least one financial instrument; determining that the last traded price is higher than a price of the outstanding unmatched offer; and based at least in part on determining that the last traded price is higher than the price of the outstanding unmatched offer, setting a starting value for the enhanced volume-weighted average price to be the price of the outstanding unmatched offer; and wherein calculating, at the point in time, the enhanced volume-weighted average price further comprises calculating the enhanced volume-weighted average price based at least in part on the starting value.
 23. An apparatus comprising: at least one processor; and at least one memory device electronically coupled to the at least one processor, in which the at least one memory device stores instructions which, when executed by the at least one processor, direct the at least one processor to at least: receive, over a duration of a sampling period, market data for at least one financial instrument, wherein the received market data comprises executed trades and unmatched orders for the at least one financial instrument, and wherein the executed trades and the unmatched orders comprise respective sizes and prices; over the duration of the sampling period, iteratively recalculate for the at least one financial instrument an enhanced volume-weighted average price based at least in part on the received market data, wherein to iteratively recalculate the enhanced volume-weighted average price comprises to: at a point in time during the duration of the sampling period, calculate the enhanced volume-weighted average price based at least in part on at least one of the received executed trades and the received unmatched orders; and at a subsequent point in time during the duration of the sampling period, calculate the enhanced volume-weighted average price based at least in part on: a) the resulting enhanced volume-weighted average price calculated at the point in time, and b) a price of another of the received unmatched orders, wherein there is a difference between the price of the another unmatched order and the resulting enhanced volume-weighted average price calculated at the point in time, and wherein an effect of the another unmatched order to adjust the resulting enhanced volume-weighted average price calculated at the subsequent point in time decreases as the difference increases; and at an end of the sampling period, communicate via a communications network to at least one computing device a last recalculated value for the enhanced volume-weighted average price.
 24. The apparatus of claim 23, wherein at each iteration, the enhanced volume-weighted average price is recalculated as: ${{trade\_ flag}*\left( \frac{\begin{matrix} \left( {{{trade\_ price}_{t}*{trade\_ size}_{t}} +} \right. \\ \left. {{eVWAP}_{t - 1}*{total\_ trade}{\_ size}_{t - 1}} \right) \end{matrix}}{{total\_ trade}{\_ size}_{t}} \right)} + {bidoffer\_ flag} + {\left( {{eVWAP}_{t - 1} + \frac{\begin{matrix} {{bid\_ flag}*\left( \frac{{bid\_ size}_{t}^{{bid\_ size}{\_ flag}}}{{total\_ trade}{\_ size}_{t}} \right)^{{trade\_ ratio}{\_ flag}}*} \\ {{bid\_ size}{\_ ratio}^{{bid\_ ratio}{\_ flag}}*\left( {{bid}_{t} - {eVWAP}_{t - 1}} \right)} \end{matrix}}{\left( {1 + {{bid\_ scaling}{\_ factor}*{{{bid}_{t} - {eVWAP}_{t - 1}}}}} \right)^{bid\_ exponent}} + \frac{\begin{matrix} {{offer\_ flag}*\left( \frac{{offer\_ size}_{t}^{{offer\_ size}{\_ flag}}}{{total\_ trade}{\_ size}_{t}} \right)^{{trade\_ ratio}{\_ flag}}*} \\ {{offer\_ size}{\_ ratio}^{{offer\_ ratio}{\_ flag}}*\left( {{offer}_{t} - {eVWAP}_{t - 1}} \right)} \end{matrix}}{\left( {1 + {{offer\_ scaling}{\_ factor}*{{{offer}_{t} - {eVWAP}_{t - 1}}}}} \right)^{offer\_ exponent}}} \right).}$
 25. The apparatus of claim 23, wherein to iteratively recalculate the enhanced volume-weighted average price over the duration of the sampling period comprises to recalculate the enhanced volume-weighted average price each time a specified time interval elapses during the duration of the sampling period.
 26. The apparatus of claim 23, wherein to receive, over the duration of the sampling period, the market data comprises to: receive at another point in time at least one of the unmatched orders; and receive at a further point in, that is subsequent to the another point in time, a change in at least one of the price and the size of the unmatched order received at the another point in time.
 27. The apparatus of claim 23, wherein to calculate the enhanced volume-weighted average price at the subsequent point in time further comprises to calculate the enhanced volume-weighted average price based at least in part on at least one weight that is applied, in part, to the price of the another unmatched order, wherein the at least one weight reduces an effect of the another unmatched order to adjust the resulting enhanced volume-weighted average price calculated at the subsequent point in time.
 28. The apparatus of claim 23, wherein the another unmatched order causes the resulting enhanced volume-weighted average price calculated at the point in time to adjust towards the price of the another unmatched order such that the resulting enhanced volume-weighted average price calculated at the subsequent point in time is closer to the price of the another unmatched order than the resulting enhanced volume-weighted average price calculated at the point in time.
 29. The apparatus of claim 28, wherein the price of the another unmatched order is lower than the resulting enhanced volume-weighted average price calculated at the point in time; and wherein the resulting enhanced volume-weighted average price calculated at the subsequent point in time is lower than the resulting enhanced volume-weighted average price calculated at the point in time.
 30. The apparatus of claim 28, wherein the price of the another unmatched order is higher than the resulting enhanced volume-weighted average price calculated at the point in time; and wherein the resulting enhanced volume-weighted average price calculated at the subsequent point in time is higher than the resulting enhanced volume-weighted average price calculated at the point in time.
 31. The apparatus of claim 28, wherein to calculate the enhanced volume-weighted average price at the subsequent point in time further comprises to: determine a first value by subtracting the resulting enhanced volume-weighted average price calculated at the point in time from the price of the another unmatched order, the first value having one of a negative sign and a positive sign; determine a second value based at least in part on the first value, the second value having the same sign as the first value; and add the second value to the resulting enhanced volume-weighted average price calculated at the point in time.
 32. The apparatus of claim 23, wherein the instructions, when executed by the at least one processor, further direct the at least one processor to at least: based at least in part on a bid-offer spread for the at least one financial instrument, determine a starting value for the enhanced volume-weighted average price; and wherein to calculate, at the point in time, the enhanced volume-weighted average price further comprises to calculate the enhanced volume-weighted average price based at least in part on the starting value.
 33. The apparatus of claim 23, wherein to calculate the enhanced volume-weighted average price at the subsequent point in time further comprises to calculate the enhanced volume-weighted average price based at least in part on a cumulative value that comprises the size of at least one of the received executed trades, wherein an effect of the another unmatched order to adjust the resulting enhanced volume-weighted average price calculated at the subsequent point in time decreases as a size of the cumulative value increases.
 34. The apparatus of claim 23, wherein to iteratively recalculate the enhanced volume-weighted average price over the duration of the sampling period further comprises to: at another point in time, calculate the enhanced volume-weighted average price based at least in part on the price of a further one of the received unmatched orders and not on the size of the further unmatched order; and at a further point in time, that is subsequent to the another point in time, calculate the enhanced volume-weighted average price based at least in part on the price and the size of a still further one of the received unmatched orders.
 35. The apparatus of claim 23, wherein the instructions, when executed by the at least one processor, further direct the at least one processor to at least: filter out from the received market data the unmatched orders having prices that are not within a predetermined price range such that the filtered out unmatched orders are not used to recalculate the enhanced volume-weighted average price over the duration of the sampling period.
 36. The apparatus of claim 23, wherein to iteratively recalculate the enhanced volume-weighted average price over the duration of the sampling period comprises to recalculate the enhanced volume-weighted average price as the market data is received over the duration of the sampling period.
 37. The apparatus of claim 23, wherein the received unmatched orders comprise at least one of bids and offers for the at least one financial instrument.
 38. The apparatus of claim 23, wherein to calculate the enhanced volume-weighted average price at the subsequent point in time further comprises to: determine a first value by subtracting the resulting enhanced volume-weighted average price calculated at the point in time from the price of the another unmatched order, the first value having one of a negative sign and a positive sign; determine a second value based at least in part on the first value, the second value having the same sign as the first value; and add the second value to the resulting enhanced volume-weighted average price calculated at the point in time.
 39. The apparatus of claim 38, wherein to calculate the enhanced volume-weighted average price at the subsequent point in time further comprises to determine a third value based at least in part on the difference between the price of the another unmatched order and the resulting enhanced volume-weighted average price calculated at the point in time; and wherein to determine the second value comprises to divide, in part, the first value by the third value.
 40. The apparatus of claim 39, wherein to calculate the enhanced volume-weighted average price at the subsequent point in time further comprises to determine a fourth value by dividing the first value by a cumulative value that comprises the size of at least one of the received executed trades; and wherein to determine the second value comprises to divide, in part, the fourth value by the third value.
 41. The apparatus of claim 40 wherein to calculate the enhanced volume-weighted average price at the subsequent point in time further comprises to determine a fifth value by multiplying the fourth value by the size of the another unmatched order; and wherein to determine the second value comprises to divide, in part, the fifth value by the third value.
 42. The apparatus of claim 23, wherein the instructions, when executed by the at least one processor, further direct the at least one processor to at least: based at least in part on a last traded price for the at least one financial instrument, determine a starting value for the enhanced volume-weighted average price; and wherein to calculate, at the point in time, the enhanced volume-weighted average price further comprises to calculate the enhanced volume-weighted average price based at least in part on the starting value.
 43. The apparatus of claim 23, wherein the instructions, when executed by the at least one processor, further direct the at least one processor to at least: determine at a start of the sampling period that: there is an outstanding unmatched bid for the at east one financial instrument, there is no outstanding unmatched offer for the at least one financial instrument, and there is a last traded price for the at least one financial instrument; determine that the last traded price is lower than a price of the outstanding unmatched bid; and based at least in part on determining that the last traded price is lower than the price of the outstanding unmatched bid, set a starting value for the enhanced volume-weighted average price to be the price of the outstanding unmatched bid; and wherein to calculate, at the point in time, the enhanced volume-weighted average price further comprises to calculate the enhanced volume-weighted average price based at least in part on the starting value.
 44. The apparatus of claim 23, wherein the instructions, when executed by the at least one processor, further direct the at least one processor to at least: determine at a start of the sampling period that: there is an outstanding unmatched offer for the at least one financial instrument, there is no outstanding unmatched bid for the at least one financial instrument, and there is a last traded price for the at least one financial instrument; determine that the last traded price is higher than a price of the outstanding unmatched offer; and based at least in part on determining that the last traded price is higher than the price of the outstanding unmatched offer, set a starting value for the enhanced volume-weighted average price to be the price of the outstanding unmatched offer; and wherein to calculating, at the point in time, the enhanced volume-weighted average price further comprises to calculate the enhanced volume-weighted average price based at least in part on the starting value. 